If you guys really want to play the weird crossover game, PSO2 just wins.
That is from the 7/11 Collaboration.
It has also collaborated with Atelier, FFXIV, Madoka Magica, Konosuba, Shining, Sonic, King of Fighters, Yozakura Quartet, Sony, Zelda, BEATLESS, Attack on Titan, Yuru Yuri, Dengeki, Famitsu, Persona 4, Persona 5, Godzilla, Vocaloid, and God knows what else I'm forgetting.
There is currently an event where the characters of Evangelion appear and you have to help them take down a copy of the 6th Angel.
In some cases, the events are just cosmetic items being introduced, but in some cases the characters actually show up with story behind them and you can get them as NPC partners (Kuro, Toro, Miku, one of the Yozakura Quartet cast, etc.), or there are event mission tied to them (Monster Hunter, FFXIV, Evangelion, etc.)
I'm half-surprised SEGA hasn't pushed for more Nintendo collaborations at this point (possibly a cross-promo with another SEGA character offered up for Smash).